In photonic devices incorporating waveguides, mode transmission is affected both by the material anisotropy, and by the cross-sectional geometry of waveguides. An example of the structures under discussion is illustrated schematically in FIG. 1. The waveguides include a core and cladding layers and generally interfaces between the core and cladding layers impose different boundary conditions for modes of propagation with different polarizations. These effects induce a polarization dependent loss (PDL), and a polarization dependent refractive index.
Modes with electrical field polarized perpendicular to the wafer plane are defined herein as TM, and parallel to the wafer plane as TE. The modal birefringence is defined as Δneff=neffTM−neffTE, where neffTM and neffTE are the effective indices for the TM-like and TE-like modes in the channel waveguide. In many types of integrated optical device, it is critical to either eliminate the birefringence altogether, or to adjust it to a given value.
Optical waveguide components and devices for communication applications are required to be polarization insensitive. As communication systems advance, the tolerance for polarization sensitivities becomes more stringent. Planar waveguide technology has made significant progress in replacing discrete photonic devices, such as thin film and bulk-optic components. The demand for increased functionality and reduced cost continues to drive the downscaling of device sizes, which can be achieved by reducing waveguide cross-section areas in high index contrast (HIC) material platforms.
Highly compact photonic devices can be implemented in high index contrast (HIC) material systems such as silicon-on-insulator (SOI), SiN on SiO2, and III–V semiconductors. In state-of-the-art commercial devices using SOI, the core size is typically on the order of 5 μm and the geometrical birefringence can be minimized to an acceptable level by changing the cross-sectional dimensions of the waveguides. This technique is sufficient for devices with large core size, since their geometrical birefringence is relatively low. Such devices, however, are of comparable size to those based on glass waveguides, and the size-reduction potential of SOI is unutilized.
One source of modal birefringence in channel waveguides is solely caused by the cross-sectional geometry of the waveguides, herewith denoted as geometrical birefringence Δngeo. As the waveguide size is reduced, Δngeo can become very large as shown in FIG. 2. Although the condition for birefringence-free propagation may still exist, the birefringence becomes very sensitive to the fluctuations in the waveguide dimensions. To achieve control within the tolerance range of state-of-the-art photonic devices, cross-sectional dimension control in the order of 10 nm is required. This stringent requirement is technologically a challenge and may be very expensive to implement. Furthermore, ridge dimensions also determine the number of waveguide modes, the minimum bend radius, and the mode size. It is often impossible to simultaneously meet several design objectives, including zero birefringence, using waveguide dimensions alone. These are some of the reasons why small-size SOI waveguide devices are not currently available commercially. Viable means of producing polarization insensitive devices or providing birefringence tuning are required.
Current practice to either eliminate birefringence, or to adjust the birefringence to a desired level (D. Dimitropoulos, V. Raghunathan, R. Claps, and B. Jalali, ‘Phase-matching and nonlinear optical processes in silicon waveguides’, Optics Express 12(1), p. 149, 2004) is to adjust the waveguide width to depth ratio (L. Vivien, S. Laval, B. Dumont, S. Lardenois, A. Koster, and E. Cassan: “Polarization-independent single-mode rib waveguides on silicon on insulator for telecommunications wavelengths”, Opt. Commun. 210, p. 43, 2002). Limitations of this method on the associated stringent requirement on dimensional inaccuracies are beginning to be recognized (Daoxin Dai, Sailing He, ‘Analysis of the birefringence of a silicon-on-insulator rib waveguide’, Applied Optics 43(5), p. 1156, 2004.
In conventional HIC waveguides where the core size is in the order of 5 μm, geometrical birefringence is on the order of 10−4. Satisfactory control can be achieved by adjusting waveguide cross-sections. This technique is sufficient for devices with large core size, since the geometrical birefringence is relatively low, waveguide modes are well confined within the core area, and generally large bend radii are used.
With reducing waveguide core size, the geometrical modal birefringence Δngeo increases drastically. The rate of change with dimensions also becomes very large. In FIG. 2, the birefringence change with waveguide dimensions is shown for an example of waveguide cross-section, but similar dependence can be found in other types of cross-sections when waveguide dimensions are reduced. By choosing the ridge aspect ratio appropriately, the birefringence may in principle be eliminated. For a given waveguide width W, an aspect ratio may exist at which the orthogonally polarized modes becomes degenerate (i.e. birefringence-free), as indicated by the circles in FIG. 3. Obviously, for waveguides with high geometrical anisotropy (e.g. for W>>H), this particular condition may not be possible to fulfill.
Ridge dimensions also determine the number of waveguide modes, the minimum usable bend radius and the mode size, as well as the birefringence. It is often impossible to simultaneously meet several design objectives, including zero birefringence, using waveguide dimensions alone.
Ridge dimensions also determine the sensitivity of birefringence to dimension fluctuations, as illustrated in an example in FIG. 3 for etch depth and waveguide width. Wide waveguides (W>H) are less sensitive to dimension changes, and offer better process latitude. Unfortunately, the condition for Δngeo=0 may cease to exist.